5 research outputs found
The General Supersymmetric Solution of Topologically Massive Supergravity
We find the general fully non-linear solution of topologically massive
supergravity admitting a Killing spinor. It is of plane-wave type, with a null
Killing vector field. Conversely, we show that all solutions with a null
Killing vector are supersymmetric for one or the other choice of sign for the
Chern-Simons coupling constant \mu. If \mu does not take the critical value
\mu=\pm 1, these solutions are asymptotically regular on a Poincar\'e patch,
but do not admit a smooth global compactification with boundary S^1\times\R. In
the critical case, the solutions have a logarithmic singularity on the boundary
of the Poincar\'e patch. We derive a Nester-Witten identity, which allows us to
identify the associated charges, but we conclude that the presence of the
Chern-Simons term prevents us from making a statement about their positivity.
The Nester-Witten procedure is applied to the BTZ black hole.Comment: Minor correction
Witten-Nester Energy in Topologically Massive Gravity
We formulate topologically massive supergravity with cosmological constant in
the first order formalism, and construct the Noether supercurrent and
superpotential associated with its local supersymmetry. Using these results, we
construct in ordinary topologically massive gravity the Witten-Nester integral
for conserved charges containing spinors which satisfy a generalized version of
Witten equation on the initial value surface. We show that the Witten-Nester
charge, represented as an integral over the boundary of the initial value
surface produces the Abbott-Deser-Tekin energy for asymptotically anti de
Sitter spacetimes. We consider all values of the Chern-Simons coupling
constant, including the critical value known as the chiral point, and study the
cases of standard Brown-Henneaux boundary conditions, as well as their weaker
version that allow a slower fall-off. Studying the Witten-Nester energy as a
bulk integral over the initial value surface instead, we find a bound on the
energy, and through it the sufficient condition for the positivity of the
energy. In particular, we find that spacetimes of Petrov type N that admit
globally well defined solutions of the generalized Witten equation have
positive energy.Comment: 43 page
Cosmological Topologically Massive Gravitons and Photons
We study topologically massive (2+1)-dimensional gravity with a negative
cosmological constant. The masses of the linearized curvature excitations about
AdS_3 backgrounds are not only shifted from their flat background values but,
more surprisingly, split according to chirality. For all finite values of the
topological mass, we find a single bulk degree of freedom with positive energy,
and exhibit a complete set of normalizable, finite-energy wave packet
solutions. This model can also be written as a sum of two higher-derivative
SL(2,R) Chern--Simons theories, weighted by the central charges of the boundary
conformal field theory. At two particular "critical" values of the couplings,
one of these central charges vanishes, and linearized topologically massive
gravity becomes equivalent to topologically massive electromagnetism; however,
the physics of the bulk wave packets remains unaltered here.Comment: 36 pages, 1 figure. v2: Expanded; exhibits localized normalizable
wave packets and exact chiral pp-wave solutions. v3: Added references;
clarification on bulk vs. boundary chirality. v4: Published version; changes
include discussion of bulk solutions' asymptotic acceptability at all m